Abstract: A cartesian to polar coordinate converter using a cordic magnitude circuit for estimating the magnitude and angle of a vector from its known orthogonal components. The vector is described in cartesian coordinates by the complex number I+jQ. The magnitude of the vector and its angle are approximated by an iterative process of successively rotating the vector toward one of the orthogonal axes and the cordic magnitude circuit is implemented in one very large scale integrated (VLSI) complementary metal-oxide semiconductor (CMOS) chip. In systems using a typical cordic magnitude circuit, accuracy increases in direct proportion to the number of rotations. The increase is accompanied by a need for an increased word size which results in a slower operating speed. The improved cordic magnitude circuit achieves higher precision without the need for a larger word size.